Ulduar: Halls of Stone
Defeat the Maiden of Grief on Heroic difficulty in one minute or less.
If you're not in epic gear and don't know how to DPS as your class, then forget about this achievement.
Your biggest enemy here is the Maiden of Grief's Shock of Sorrow, a spell with a 4-second cast time that puts a 6-second damage-breakable incapacitation on the entire party. As she is casting Shock of Sorrow, stand in the black circles (Storm of Grief) that she casts earlier. One tick of damage from standing in the Storm is enough to break the incapacitation effect.
Depending on how much damage you can deal per second, the Maiden can cast this spell one to four times. That's a maximum of 24 seconds wasted if you can't put her out of her misery quickly enough.
Brann Spankin' New
Defeat the Tribunal of Ages encounter on Heroic difficulty without allowing Brann Bronzebeard to take any damage.
Take a Death Knight or Paladin for tanking. Use the stairs at the entrance to the Tribunal's room as a choke point to gather all of the adds before they can reach Brann. Hunters should drop Frost Traps to give the tank time to pick up everything.
Now just avoid the lasers and the giant black ball and you'll be fine. If you wipe, you can attempt this achievement again.
And no, healing Brann to full health after he's taken damage will not work.
Abuse the Ooze
Defeat Sjonnir the Ironshaper on Heroic difficulty and kill 5 Iron Sludges during the encounter.
Tank Sjonnir in the corridor you entered from and bring him down to 40-50% of his HP. When he starts casting Lightning Ring, get away from him and focus on the oozelings that start spawning. Leave them alone until they get to the middle of the room and merge into an Iron Sludge. Destroy this Iron Sludge before more spawn or suffer the AoE poison volleys that can rape your party.
Once you've destroyed the 5 sludges, Sjonnir can join them.
Ulduar: Halls of Lightning
Defeat General Bjarngrim on Heroic difficulty while he has a Temporary Electric Charge.
Before the fight, Bjarngrim moves around the other half of the room, casting Temporary Electric Charge on himself. This powers up any adds that are near him, so clear one of the platforms and the bridges next to it before starting the fight.
Bjarngrim and his adds gain a 30% increase to their damage as long as they have the Temporary Electric Charge. If Whirlwind hurt your DPS classes before, it will downright kill them if they don't back off quickly enough.
Defeat Volkhan on Heroic difficulty without allowing him to shatter more than four Brittle Golems.
Ignore the golems that spawn through the fight and attack Volkhan if he goes down. The golems only do around 2-3,000 damage per hit. Unless you're in grays and whites, this shouldn't be that hard.
Defeat Loken on Heroic difficulty in two minutes or less.
You don't have to worry about stuns, but Loken's Lightning Nova may have you running for your life, shaving 5-10 seconds off your attack time.
If you're tough, your group can stand next to Loken and suck up the damage. Have around 20,000 HP to guarantee your survival and you should be fine.
Caverns of Time: Culling of Stratholme
Kill 100 Risen Zombies in one minute.
Take a Paladin tank with you for this one.
Fight through the encounter until Salramm the Fleshcrafter spawns. Take him all the way to the inn in the northeast area and tank him inside. Kill all the zombies that attached themselves to your group and wait for three minutes. Once the zombies outside the inn have respawned, kill Salramm.
Arthas will order you to meet him at the inn, but he's an incredibly slow runner when he's not in your visual range, so go make a sandwich.
Kill the third boss and then open the path to the burning alley. Have your Paladin tank return to the first area. Remove any reactive damage effects like Thorns before pulling all of the zombies in the first area. There should be around 70 or so there. Once the zombies have been pulled, run back to the burning alley and wait for the crowd of shamblers to appear on your map. Once the majority of the zombie train is in the burning alley, take them all out with area-of-effect attacks. Any remaining zombies that need to be dispatched can be found in the burning alley.
Remember Rule #1 when pulling zombies: Cardio.
The Culling of Time
Defeat the Infinite Corruptor on Heroic difficulty.
After Mal'ganis turns all of Stratholme into an undead carnival, you have 25 minutes to clear your way through 8 waves of Scourge monsters, 3 bosses and a burning alley laden with more Scourge freaks and zeds. Once you've passed the burning alley, take a left at the marketplace to find the Infinite Corruptor erasing one of the Bronze Dragonflight from existence.
The Infinite Corruptor can leave in the middle of the fight, so save yourself at least 3 minutes to kill him.
Depending on how quickly you work, you can allot one or two wipes for this.